In Marvel comics Attilan is the home city of the home city of the Inhumans. It is a very advanced technological city that is capable of flying and moving around the universe. The city will make its first appearance in the MCU with the show / film Inhumans that will be released in Imax theaters. For pictures of the Attilan in the MCU scroll to the bottom of this page in the MCU section.

The Inhumans come from humans who were experimented on by the Kree aliens. Due to their unique attachment to the Kree they have far higher amounts of technology than their human cousins. They used this technology to create a very advanced city. The city is capable of moving vast distances and could be thought of as a big city sized, space ship.

The city created by ancient Inhumans has been located on various places in Earth. The Inhumans have continually move it to keep it away from humans.

Its name is derived from Alantis which at the time of its creation (7000 years ago) was the former great civilization on the planet.

Structure:
The city is large and houses multiple levels that are generally organized along with the castes of Inhuman society.
The top floor is for Inhuman royal family whose palace resides high into the skyline. The rest of the open air level of the city contains those in the high to mid caste of the society as determined by how they changed in the terrigen mist or those who have not yet been exposed.

The lower levels are where the lower cast members reside. These members are primarily made up of the Alpha Primitives. This is a group who reacted poorly to the Terrigen mist and de-evolved.

The important Terrigen mist and the crystals from which it comes from are also housed within Attilan.

Location -
The city of Attilan while capable of movement has recently been residing in an area of Earth's moon called the Blue area of the Moon. The Blue Area of the moon is an ancient city created long ago by the Kree aliens and has atmosphere.

Attilan has traveled to places on Earth at various points in history including the Himalayas and under the Pacific Ocean. Generally, the Inhumans park the city in a remote location to avoid contact with their human cousins. Inhumans fear both tampering with their way of life as well as disease. While Inhumans are stronger than humans their immunities are far weaker making them very vulnerable to everyday human diseases.

There is also a fear that the lower castes of Inhuman society could rebel while seeing other ways of living. For both of these reasons the city is often kept far away from large human population centers.

There is also a fear of humans themselves who could in their vast numbers harm the Inhumans.

While the Inhumans with their vast powers could potentially take over human kind they generally seem disinterested by this concept. Some Kings and villains like Maximus the Mad have proposed world conquest but they are normally taken down by other Inhumans.

Intestellar Travel
Attilan has also traveled to another galaxy to the planet of Hala where the Inhumans effectively took control of the Kree Empire.
This was not a typical capability of Attilan, as it typically moved slowly around the Earth or to Earth's moon. The vast speed at which Attlilan traveled was made possible by using older interstellar engines infused with the power of Black Bolts voice. The voice of Black Bolt was also harnessed as a weapon that destroyed an Armada of Skrulls and Shi'ar on its route to the throne world of the Kree Empire of Hala.

Here is a nifty map of Attilan. Here you can see that the Palace of the Royal Family is the central and more prominent feature of the city.
The lower cast of Alpha Primitives live on a lower level of the city.

Places of Interest:

Palace of the Royal Family - This is where the rulers of the Inhumans reside and make decisions.

Terrigen Lab/Chambers (Mentioned in Realm of Kings: Inhumans #1) - Stores the Terrigen mists that is used for Terrigenesis the process that gives Inhuman's their powers. I believe the basement portion is called the Terrigen Chambers and contains the crystals. The Terrigen mists rise from the crystals and are stored in the Terrigen Lab. The Terrigen Lab is also very near the Royal Palace which speaks to the chemicals importance in Inhuman Society.

Arena of Judgement - Place where Inhumans battle to determine right and wrong. Similar to a Roman Colosseum.

Tomb/Temple/House of Randac - Where King Randac who invented Terrigesis process rests. This is a revered and sacred place. This is the place where King Randac first experimented on himself and
other Inhumans creating the Terrigensis process. This housed
individualized chambers for Inhumans to undergo the Terrigenesis process
in. (Seen in Uncanny X-Men: First Class #1) For more on the temple see: --> What is the Temple of Randac?

Entrance to the Pit of the Dead - This is where the dead are lowered. It is considered hallowed ground by the Inhumans (Mentioned in: Inhumans: The Great Refuge #1)

Not shown on Map but still important:Weeping Tower / Tower of Wisdom- Houses monks who trained Karnac in his martial skills. (X-Men First Class #2)

Recent Events:
In the story of Inhumanity the city of Attilan crashes down to Earth.

MCU

The city will make its first appearance in the MCU with the show / film Inhumans that will be released in Imax theaters.

Marvel released a short teaser for the show of Inhumans that featured a structure in a dark setting with lights off in the distance. My assumption is that this setting is part of Attilan. Some have said they think it is from a prison cell that houses Maximus the Mad. Maximus is a narrator of the clip so this is possible.